Quantization of line bundles on lagrangian subvarieties
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We apply the technique of formal geometry to give a necessary and sufficient condition for a line bundle supported on a smooth Lagrangian subvariety to deform to a sheaf of modules over a fixed deformation quantization of the structure sheaf of an algebraic symplectic variety.
Mathematics Subject Classification53D55 14D21
We are grateful to Dima Arinkin for helpful remarks and to Pierre Schapira for historical comments. The first author was supported by a Simons Foundation Collaboration Grant. The second author was supported in part by the NSF Grant DMS-1001677. The third author was partially supported by the RFBR Grant 12-01-33024, Russian Federation Government Grant, ag. 11.G34.31.0023, and the Dynasty Foundation Award. The fourth author would like to thank K. Behrend and B. Fantechi for many inspiring discussions on quantization. He is grateful to the Mathematical Science Research Institute, Berkeley, for hospitality during his stay in the Spring of 2013. The work on the paper was also partially supported by the NSF Grant DMS-0932078 000.
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